Let Y be a gpower-normal random variable and X=gpowerY;p the transformed variable distributed as TNμX,σ2,−1/p,∞. Let xα be the α-quantile for X, to obtain an expression for the quantiles of a truncated normal distribution we proceeded as follows: PX≤xα=PX0≤xα−FX0−1/p=1KΦxα−μXσ−Φ−1/p−μXσ=1KΦxα−μXσ−1−K=α, where X0∼NμX,σ is the corresponding normal variable with cumulative distribution FX0 and Φ is the cumulative distribution of the standard normal. Now, clearing up xα=σΦ−1K(α−1)+1+μX.